∫∫(4-x-y)dxdy积分区域D为x^2+y^2

原式=∫dθ∫(4-rcosθ-rsinθ)rdr (作极坐标变换)=∫dθ∫[4r-r^2(cosθ+sinθ)]dr=∫[8(sinθ)^2-(8/3)(sinθ)^3cosθ-(8/3)(sinθ)^4]dθ=∫[3-(8/3)cos(2θ)-(1/3)cos(4θ)-(8/3)(sinθ)^3cosθ]dθ=3π....